Problem: Rewrite as a simplified fraction. ${2.90\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2903.3333...\\ 100x &= 290.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2613}$ ${x = \dfrac{2613}{900}} $ ${x = \dfrac{871}{300}} \text{or} {2 \dfrac{271}{300}}$